Thats the last thing I would do!
Recording the screen while your video plays will kill the original video quality - not sure why on earth you would want to do this when you can simply add an audio track alongside the original video while keeping its original quality.
GoPro Studio for ease of use. Audacity for just audio recording. Davinci Resolve if you want to make it easier to sync and maybe do some more editing down the road. But beware Davinci Resolve has a bit of a learning curve.